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 A218858 Number of Gaussian primes at taxicab distance n from the origin. 5
 0, 0, 4, 12, 0, 16, 0, 20, 0, 16, 0, 28, 0, 24, 0, 32, 0, 32, 0, 36, 0, 24, 0, 36, 0, 64, 0, 32, 0, 48, 0, 44, 0, 32, 0, 72, 0, 64, 0, 48, 0, 72, 0, 60, 0, 56, 0, 60, 0, 40, 0, 56, 0, 72, 0, 112, 0, 64, 0, 76, 0, 88, 0, 56, 0, 136, 0, 92, 0, 80, 0, 76, 0, 88, 0 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 COMMENTS Except for n = 2, there are no Gaussian primes at an even taxicab distance from the origin. All terms are multiples of 4. See A218859 for this sequence divided by 4. The arithmetic derivative of Gaussian primes is either 1, -1, I, or -I. LINKS T. D. Noe, Table of n, a(n) for n = 0..10000 T. D. Noe, Linear plot EXAMPLE In the taxicab distance, the four Gaussian primes closest to the origin are 1+I, -1+I, -i-I, and 1-I. The 12 at taxicab distance 3 are the four reflections of 3, 2+I, and 1+2I. MATHEMATICA Table[cnt = 0; Do[If[PrimeQ[n - i + I*i, GaussianIntegers -> True], cnt++], {i, 0, n}]; Do[If[PrimeQ[i - n + I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 0, -1}]; Do[If[PrimeQ[i - n - I*i, GaussianIntegers -> True], cnt++], {i, 1, n}]; Do[If[PrimeQ[n - i - I*i, GaussianIntegers -> True], cnt++], {i, n - 1, 1, -1}]; cnt, {n, 0, 100}] CROSSREFS Cf. A055025 (norms of Gaussian primes). Cf. A222593 (first-quadrant Gaussian primes). Cf. A225071, A225072 (number of terms at an odd distance from the origin). Sequence in context: A180057 A222316 A255383 * A014458 A099733 A073902 Adjacent sequences:  A218855 A218856 A218857 * A218859 A218860 A218861 KEYWORD nonn AUTHOR T. D. Noe, Nov 12 2012 STATUS approved

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Last modified October 21 08:47 EDT 2019. Contains 328292 sequences. (Running on oeis4.)